The Sensitivity of the Radiation Budget in a Climate Simulation to Neglecting theEffect of Small Ice Particles

FAISAL S. BOUDALA

Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada

GEORGE A. ISAAC

Cloud Physics and Severe Weather Research Section, Environment Canada, Toronto, Ontario, Canada

N. A. MCFARLANE AND J. LI

Canadian Centre for Climate Modelling and Analysis, Environment Canada, Victoria, British Columbia, Canada

(Manuscript received 18 August 2005, in final form 19 September 2006)

ABSTRACT

The sensitivity of the atmospheric radiation budget to ignoring small ice particles (D � 100 �m) inparameterization of the mean effective size of ice particles was investigated by using the Canadian Centrefor Climate Modelling and Analysis (CCCma) third-generation general atmospheric circulation model(AGCM3). The results indicate that small ice particles play two crucial roles in the radiative transfer thatinfluence the simulated climate. First, they inhibit the IR radiation from escaping to space and, second, theyenhance the scattering of solar radiation. On average, these two effects tend to partially cancel each otherout. However, based on AGCM simulations, the small ice crystals make clouds more opaque to IR radia-tion. Generally, 5-yr seasonally averaged GCM results suggest that the strongest anomalies in outgoinglongwave radiation (OLR) are found in the Tropics, reaching 15 to 25 W m�2 in areas where cold high cirrusanvil clouds are prevalent. The global average change in net cloud radiative forcing was 2.4 W m�2 inJune–August (JJA) and 1.7 W m�2 in December–February (DJF). The change in globally averaged 5-yrmean cloud forcing was close to 1.9 W m�2. When the small particles were included, the globally averaged5-yr mean precipitation decreased by about 8%, but cloudiness increased only slightly (by 2%). The 5-yraveraged global mean surface (screen) temperature also increased slightly (about 0.2°C) when the small iceparticles were included.

1. Introduction

Atmospheric general circulation models (AGCMs)require solar and terrestrial infrared (IR) radiation tobe calculated accurately in order to simulate climate.Ice clouds play a major role in the earth’s climate byabsorbing the IR radiation and reflecting the solar ra-diation (Ramanathan et al. 1983; Ramaswamy and Ra-manathan 1989; Stephens et al. 1990). The interactionsof radiation with ice clouds are incorporated throughparameterization of single scattering properties interms of mean effective sizes (Dge) of ice crystals andsome other microphysical variable such as ice water

content (IWC; e.g., Ebert and Curry 1992; Fu 1996; Fuet al. 1998) that are predicted by GCMs. However, Dge

is not predicted by most GCMs, but it is inferred frompredicted microphysical variables. Therefore, accurateparameterization of effective sizes of ice crystals interms of microphysical variables available in theAGCM is crucial for climate studies.

There are various definitions of the effective size ofice particles as summarized by McFarquhar andHeymsfield (1998) and Wyser (1998). In this paper, Dge

is defined following Fu (1996) as

Dge �2�3 IWC

3�iAc, �1�

where �i is the density of pure ice, and Ac is the meancross-sectional area of ice particles per unit volume.These microphysical variables are normally determined

Corresponding author address: Dr. Faisal Boudala, Cloud Phys-ics and Severe Weather Research Section, Environment Canada,Toronto, ON M3H-5T4, Canada.E-mail: Faisal.Boudala@ec.gc.ca

15 JULY 2007 B O U D A L A E T A L . 3527

DOI: 10.1175/JCLI4191.1

JCLI4191

based on in situ measurements of the ice particle sizedistribution. There are parameterizations of Dge, whichare developed based on such in situ observations thatconsider small ice particles (e.g., Boudala et al. 2002;Ivanova et al. 2001; McFarquhar 2001; McFarquhar etal. 2003). The effective size of ice particles has also beenparameterized based on direct in situ measurements ofIWC and Ac (or extinction coefficient; Garrett et al.2003). There are also parameterizations of a bimodalsize distribution of ice particles as a function of IWCand temperature, and thus Dge can be derived providedthat IWC and temperature are known (e.g., Ivanova etal. 2001; McFarquhar and Heymsfield 1997). However,the determination of these quantities based on aircraftmeasurements using the current particle-measuringprobes is still a challenge. The ice particle sizes andconcentrations are normally measured using probessuch as the Particle Measuring System (PMS) 2D opti-cal array probes (2D-C and 2D-P) and the ForwardScattering Spectrometer Probe (FSSP) cloud dropletprobe. The PMS 2D-C and 2D-P probes measure con-centrations in the particle size ranges of 25–800 and200–6400 �m, respectively.

The 2D optical array probe was developed almost 36yr ago by Knollenberg (1970). The instrument has beenused in the cloud physics community ever since. Al-though the actual imaging method remains the same,the algorithms for data extraction methods such as cor-rectly sizing, counting, and identifying the shapes ofparticles are continuously evolving. It is now wellknown that the small particles (D � 100 �m) are notwell measured using the traditional 2D-C probe due tomany problems in identifying and sizing the particles(e.g., Korolev et al. 1998a). It has also been known forsome time that there are problems with measuring thelarge ice particles because of things like particle shat-tering due to collisions with the probes themselves(Cooper 1977). This issue has been a subject of somediscussions in the latest works of Korolev and Isaac(2005) and Field et al. (2006). Field et al. have identifiedthat the particle shattering effects become significantwhen the mass weighted mean size exceeds 1 mm andthe particle size distributions are relatively broad. How-ever, because of the fact that there are many correc-tions to be made as mentioned earlier, the exactamount of the errors associated with particle shatteringis difficult to quantify. One way to exclude the shat-tered particles is by removing all particles crossing thesampling volume in unusually short interarrival timesor short distances between two successive images asdiscussed by Field et al. (2006) and earlier by Cooper(1977). Some of the old image processing software al-

ready have such algorithms. However, the precipitationprobes such as 2D-P with a larger sample volume andcourse resolution tend to naturally filter out the shat-tered particles; thus it is the 2D-C probe that is affectedthe most in the presence of shattered particles (seeField et al. 2006).

An earlier study by Gardiner and Hallett (1985) in-dicated that the FSSP probe measured ice concentra-tions 2–3 orders of magnitude higher than those derivedfrom a replicator. However, a recent study by Arnott etal. (2000) suggests that the replicator underestimatesconcentrations of particle (D � 50 �m) and thus cannotbe compared with the FSSP data. A more recent studyby Field et al. (2003) also suggests that the FSSP probemay overestimate ice concentration, but on averageonly by a factor of 2 due to shattering of ice particles.

There are also considerable uncertainties in deter-mining the IWC from observed particle size distribu-tions or direct measurements. As a result of these prob-lems, developing an accurate and widely applicable pa-rameterization of Dge has been a great challenge.Typically parameterizations are developed based onmeasurements conducted in a particular region or me-teorological regime (e.g., tropical or extratropical re-gions) and thus may not be appropriate to be used forthe entire globe. In this research, “small ice particles”refers to the ice particle sizes (D � 100 �m) that are notreliably measured with the current available instru-ments such as the PMS 2D-C and 2D-P probes, but thisdefinition may differ for other researchers. The methodfor determining the size spectra from small to large iceparticles, recognizing all the above problems, has beendescribed by Boudala et al. (2002), and a brief summaryis given in section 2.

Small ice crystals can be important for both solar andthermal IR radiative transfer (Platt et al. 1989; Kinne etal. 1992). In the geometric optics limit, the extinction ofradiation is largely determined by the cross-sectionalarea (A) of ice particles projected normal to the propa-gation direction of the radiation. The absorption of so-lar radiation, however, is determined by both IWC andA. Therefore, the addition of the small particles en-hances both scattering and absorption. The addition ofsmall ice particles increases both Ac and IWC leading tocounteracting effects on Dge in accordance with Eq. (1).However, it has been shown using in situ measurementsin extratropical stratiform clouds that the net effect ofadding small ice particles is to decrease Dge on averageclose to 40% (Boudala et al. 2002).

The effect of adding small particles on IR radiationcannot be explained solely based on the geometric op-tics approximation as has been done for solar radiation,

3528 J O U R N A L O F C L I M A T E VOLUME 20

particularly for particle sizes (D � 40 �m) that aretypically found in the natural atmosphere (e.g., Yang etal. 2001; Chýlek et al. 1992; Fu et al. 1998). When smallice particles are added to the larger ice crystals, it hasbeen found that for some IR wavelengths, the scatter-ing cross section is larger than the enhanced absorption,and the opposite occurs for the other IR wavelengths(Stackhouse and Stephens 1991). Generally in the IRwavelength that exhibit strong absorption, the absorp-tion cross section is more closely related to A. In thecase of weak absorption, the absorption cross section isrelated to particle volume or mass. Since the addition ofsmall ice particles more significantly affects A than themass, the general tendency of adding small ice particlesis to increase absorption (Foot 1988; Stackhouse andStephens 1991). However, it should be noted that theeffect of neglecting small ice particles on the radiationbudget depends on the sizes and amount of these par-ticles present in natural clouds (Arnott et al. 1994), andthis is not well known at this time due to limitations ofthe measurements as mentioned earlier. Using obser-vations in tropical cirrus clouds, Heymsfield and Mc-Farquhar (1996) found that smaller ice particles (D �

90 �m) make up more than 50% of the mass and areresponsible for more than 50% of the extinction in theupper colder parts of cirrus. However, in the lowerwarmer region, they found that large ice crystals domi-nated the cloud and small particles were only respon-sible for 10% of the extinction. Nonetheless, they ig-nored the contribution of small ice particles in the pa-rameterization of cloud optical properties. Using a2-km-thick idealized cirrus cloud, Fu and Liou (1993)showed that decreasing Dge from 50 to 25 �m increasedIR heating (cooling) by a factor of 2 at the base (top) ofcloud with a little change in solar heating. They alsoshowed that the net cloud forcing at the top of theatmosphere (TOA) due to this change is positive andincreases with decreasing Dge, except for Dge � 25 �mand IWP 20 g m�2 where the forcing may be nega-tive. A study of the radiative effects of small ice par-ticles, conducted by simulating stratiform anvils in theupper tropical troposphere using a one-dimensionalcloud model, showed that neglecting small ice crystals(D � 20 �m) could amount to an uncertainty of 40 Wm�2 in the diurnally averaged net cloud forcing at thetop of the atmosphere (Zender and Kiehl 1994) due toa significant increase in solar albedo. Also, the climatesensitivity study conducted by McFarquhar et al. (2003)shows that changing effective radius from 30 to 10 �mamounts to a 25% increase in shortwave forcing atTOA and at the surface. Although there have beensome studies of the effect of small particles based onsome idealized cirrus clouds or assumed variation in

mean size of ice particles, the radiative impact of ne-glecting small ice particles in GCMs has not been con-sidered explicitly. Although the actual contribution ofsmall ice particles is not accurately known, it is worth-while to test the sensitivity of neglecting these particlesin parameterizations of Dge based on the currentlyavailable measurement information.

As noted above, based on in situ observations, Bou-dala et al. (2002) developed parameterizations of themean effective size of ice particles as a function of icewater content and temperature, and temperature alone,with and without small ice particles (D � 100 �m). Thepurpose of the present work is to study the sensitivitiesof the radiation budget and climate simulations to thesedifferent parameterizations. The sensitivity of climatesimulations will be studied using 5-yr simulations withthe third-generation atmospheric general circulationmodel (AGCM3) of the Canadian Centre for ClimateModelling and Analysis (CCCma).

2. The CCCma AGCM

The CCCma AGCM3 is used to investigate the cli-mate impact of small ice particles. This model, a suc-cessor to AGCM2 described by McFarlane et al. (1992),is documented by McFarlane et al. (2005). The descrip-tion provided here summarizes features of relevance tothe present work, particularly in regard to the repre-sentation of clouds and radiation.

The horizontal spatial structure of the main prognos-tic variables in AGCM3 are represented by the spectraltransform method similar to AGCM2 while the verticalstructure is represented by rectangular finite elementsdefined for hybrid vertical coordinates (Laprise and Gi-rard 1990). The operational version of this model (usedin the present work) has 32 layers extending approxi-mately up to 50 km above the surface or 1 hPa andemploys a triangular 47-wave spherical harmonics rep-resentation (T47). Sea surface temperatures and sea iceextent and concentration are specified using seasonallyvarying climatological data. Surface exchanges of heat,moisture, and momentum are parameterized followingAbdella and McFarlane (1996). Atmospheric convec-tion is parameterized by a cumulus parameterization asdescribed by Zhang and McFarlane (1995). Cloudcover is specified as a function of relative humidity andpotential temperature stratification. The cloud watercontent is assumed to be proportional to the adiabaticvalue found by vertically lifting a parcel of air througha specific depth (Betts and Harshvardhan 1987) similarto AGCM2. The zonal mean distribution of back-ground aerosol (sulfate, dust, and sea salt) is imple-mented based on Shettle and Fenn (1979).

15 JULY 2007 B O U D A L A E T A L . 3529

The solar radiation part of this model is based onFouquart and Bonnel (1980) with an extension fromtwo spectral bands to four spectral bands. For gaseoustransmission, O3, water vapor and CO2 are consideredin the solar radiation, but the absorption of O2 is notconsidered. Rayleigh scattering is considered in all fourbands from spectral range 0.25 to 4 �m. The infraredradiation part is based on Morcrette (1991) with sixbands covering from spectral range 4 to 1000 �m. Wa-ter vapor, CO2, O3, CH4, N2O, CFC12, and CFC11

are contained in the gaseous transmission. The watervapor continuum is based on a parameterization byZhong and Haigh (1995). This water vapor continuumscheme is based on the results of line-by-line model(LBLRTM) Clough–Kneizys–Davies Model version 2.2(CKD2.2; Clough et al. 1989).

The water cloud optical properties are parameterizedbased on Dobbie et al. (1999) for solar radiation andChýlek et al. (1992) for the infrared. The ice wateroptical properties are parameterized following Fu(1996) for solar radiation and Fu et al. (1998) for theinfrared. In the original radiation algorithm in GCM3,the mean effective size (Dge) of nonspherical ice crys-tals was defined in terms of IWC based on Lohmannand Roeckner (1996). This parameterization will alsobe briefly discussed in the sections below.

The parameterization of the mean effective size ofice particles used for this study is based on Boudala etal. (2002) and given as

Dge � 60.1 exp�0.008T � �2�

and

Dge�s � �46.4 exp�0.015T �

or

53.01 IWC0.06 exp�0.013T �� , �3�

without [Eq. (2)] and with small ice particles [Eq. (3)],respectively, where T is temperature in °C and IWC isg m�3. The parameterizations given in Eqs. (2) and (3)were based on data collected during several fieldprojects conducted in extratropical regions. The maininstruments used for this work includes the PMS 2D-C,2D-P, and FSSP probes discussed earlier, and the Nev-zorov total water content (TWC)/liquid water content(LWC) probes (Korolev et al. 1998b). The shatteredand elongated thin particle images (D � 100 �m) aremainly excluded from the 2D-P and 2D-C data usingimage processing software. The small particles (D �

100 �m) are estimated using the FSSP concentrations,and 2D-C spectra. The FSSP spectra are assumed to bedescribed by a gamma distribution function and overlapwith 2D-C spectra at 125 �m where the 2D-C measure-

ment is reliable. When the gamma distribution functiondescribing the FSSP spectra is integrated, it was set togive the concentration measured with the FSSP probecorrected for shattering effects (Field et al. 2003). Onlysizes between 125 and 575 �m have been included from2D-C measurements, and the rest of the sizes greaterthan 575 �m are derived from 2D-P measurements.Thus based on the discussion presented earlier, theshattering effects on the parameterizations are not ex-pected to be that significant. The total mass derivedfrom the total spectra (small � large) agreed quite wellwith the IWC measured independently with the Nev-zorov probe, particularly at higher IWCs, which vali-dates the parameterizations. The recent work by Isaacet al. (2006) reveals that the Nevzorov probe “may”also suffer from similar shattering problems, but theywere unable to quantify the problem; more studies areneeded to evaluate the implications of this for the pa-rameterizations used in this paper. A detailed discus-sion of the development of the parameterization isgiven in Boudala et al. (2002). As noted below, the Dge

parameterization agrees quite well with that reportedrecently by Garrett et al. (2003) when small particlesare included. It is noteworthy that Garrett et al. utilizeddirect measurements of IWC and extinction in theTropics, which is different from the measurementmethods used by Boudala et al. Thus, notwithstandingthe measurement uncertainties and the fact that the twoindependently proposed parameterizations were devel-oped based on measurements in different geographicalregions, their similarity is encouraging. It justifies theuse of a single parameterization for the entire globe forthe present study since a central goal is to gain insightinto the sensitivity to representations of Dge in climatesimulations and in particular the possible importance ofaccounting for small particles. Considerable uncer-tainty remains as to the range of applicability of theseparameterizations, and there are circumstances inwhich they would not be adequate. Other studies haveshown that the mean effective sizes of ice particles insome tropical cirrus cloud regimes (e.g., McFarquhar2001) are relatively larger than the extratropical regions(e.g., Boudala et al. 2002). In these particular cloudregimes, the effective size is likely to depend morestrongly on variables (such as IWC and number con-centration) that are typically either specified a priori orare less reliably simulated by current GCMs. For ex-ample, in AGCM3, IWC is generated through a simpli-fied bulk parameterization of microphysical processesthat does not depend explicitly on particle sizes. There-fore, the model-predicted IWC is assumed to representthe total IWC that includes the small ice particles.

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3. Sensitivity experiments

The numerical experiments discussed below were de-signed to study aspects of the sensitivity of climatesimulations to specification of the effective size of icecrystals in clouds. Equation (2) was used to representthe case without small ice particles, and Dge dependsonly on T. Equation (3) was used to represent the casewith small ice particles and includes relationships whereDge depends on T alone and on both T and IWC. In theoperational version of AGCM3, the mean effective sizeparameterization of ice particles is based on that usedby Lohmann and Roeckner (1996), which is given asDge � 129 IWC0.216, but limited to be no smaller than 31(�m) and not allowed to exceed 77 (�m). The effect ofusing this parameterization will be compared with theresults from using the parameterizations of the meaneffective size based on Boudala et al. (2002) that aregiven in Eqs. (2) and (3). As noted above, it is assumedthat the model-predicted IWC represents the totalIWC, no matter what parameterization is used.

Two different interactive simulations have been con-ducted. Interactive simulations were chosen in prefer-ence to offline radiation budget calculations in order toaccount for the roles of feedback effects associated withneglecting small ice particles in climate simulations.One of the simulations is to test the sensitivity to ne-glecting small crystals. For this test, the parameteriza-tion of mean effective ice crystal size was done withoutand with small particles, Dge(T) and Dge�s(T), and isapplied for the entire globe during a 5-yr GCM simu-lation. The second experiment is to evaluate some keyfeatures of the climate simulations using the proposedparameterization against observations and relative to acontrol simulation using the standard operational pa-rameterization. For this experiment, one 5-yr simula-tion with Dge�s(IWC, T) that includes small particleshas been conducted.

a. Sensitivity in the IR radiation and comparisonwith satellite observations

Figure 1 shows the mean seasonal difference{FIR[(Dge(T)] � FIR[(Dge�s(T)]} in simulated outgoinglongwave radiation (OLR) at the TOA based on a 5-yrsimulation. The three panels are for June–August(JJA), September–November (SON), and December–February (DJF). Generally, the largest differences inOLR are found in the Tropics reaching 15 to 25 W m�2

in areas where convective clouds that are associatedwith the intertropical convergence zone are commonlyfound. These anomalies seem to propagate northwardin JJA and southward in DJF. The anomalies are alsomostly positive, which implies that in the absence of

small ice particles, the atmosphere is more transparentto IR radiation. Figure 2 shows the vertical cross sectionof anomaly in cloudiness for JJA (top panel) and DJF(bottom panel). It is interesting to note that the mostpronounced cloudiness anomaly in the upper tropo-sphere is negative and flanked below by broader andgenerally much less pronounced positive anomalies, im-plying that the most pronounced effect of accountingfor small ice particles is increasing cloudiness in theseupper-tropospheric regions. The pronounced decreasesin cloudiness flanking the increases in the tropical up-per troposphere are indicative in part of an upwardshift in cloudiness associated with accounting for theeffects of small particles. As noted in the precedingsection, the cloud cover is diagnosed based on model-predicted relative humidity and thermal stratification.Generally the changes in both temperature and relativehumidity are small in the upper troposphere but incombination are responsible for the changes in cloudi-ness. For example, there are small but systematic in-creases in relative humidity (not shown) in the tropicalupper troposphere associated with accounting for thecontribution of small particles to the effective size pa-rameter. Changes in cloudiness particularly in the lowertroposphere are generally small. Although changes inOLR and cloudiness are generally consistent, the directeffect associated with the change in the effective sizedue to adding small ice particles seems to be mainlyresponsible for the IR changes depicted in Fig. 1. Theinclusion of small particles can enhance both the cloud-top cooling and cloud-base warming because the de-crease in effective size increases both absorption andemission of IR radiation. However, the cooling effect isrelatively stronger, resulting in a net reduction in OLRwhen the small ice particles were included. Similar re-sults have been found by Stackhouse and Stephens(1991).

As noted above, the OLR changes are most pro-nounced in the Tropics. This is consistent with thechange in the effective ice crystals size due to addingsmall ice crystals in relation to temperature, shown inFig. 3. The small ice particle contribution increases withdecreasing temperature reaching up to 50% at verycold temperatures. The ice clouds in the tropical upperatmosphere are found at much higher levels and muchcolder temperatures than the clouds found in the highlatitudes and are responsible for much of the IR forcing(Hartmann et al. 1992). This is consistent with obser-vations during the International Cloud ClimatologyProject (ICCP) (Doutriaux-Boucher and Seze 1998)and satellite observations (Riedi et al. 2000), which in-dicate that the frequency of occurrence of cold iceclouds tends to be a maximum in the area of the inter-

15 JULY 2007 B O U D A L A E T A L . 3531

FIG. 1. Global distributions of anomaly {FIR[(Dge(T )] � FIR[(Dge�s(T )]} for outgoing longwaveradiation at the top of the atmosphere based on a 5-yr simulation: (a) JJA, (b) SON, and (c) DJF.

3532 J O U R N A L O F C L I M A T E VOLUME 20

Fig 1 live 4/C

tropical convergence zone. As a result of this, the effectof adding small ice particles to the IR flux at the top ofthe atmosphere is likely to be much more pronouncedin the Tropics as compared to the high latitudes, reach-ing 15 to 25 W m�2 within the intertropical convergencezone. As noted above and illustrated in Fig. 3, the Gar-rett et al. (2003) tropical parameterization of Dge

(G2003) is very similar to Dge that includes small par-ticles. It is interesting to note that in the DJF season(Fig. 1c), the negative anomaly in the OLR over thetropical Pacific Ocean is associated with a relatively

strong positive anomaly in planetary albedo shown inFig. 4. This change is associated both with changes inthe upper-tropospheric cloudiness and changes in effec-tive size in those regions, and is consistent with thechanges in shortwave cloud forcing discussed in the fol-lowing section.

Figure 5 shows zonal and seasonally averaged IRcloud forcing at the TOA in DJF. The satellite obser-vations based on Earth Radiation Budget Experiment(ERBE) data (see Barkstron 1984) are marked asdashed lines. In broad accord with observations, the

FIG. 2. The vertical cross section of the simulated cloudiness anomaly for (top) JJA and (bottom)DJF.

15 JULY 2007 B O U D A L A E T A L . 3533

simulated cloud forcing peaks in areas where significantclouds are formed in association with well-known fea-tures of the general circulation of the atmosphere. TheIR cloud forcing due to adding small ice crystals is pro-nounced in these cloudy regions and consistent with theOLR anomalies depicted in Fig. 1. It must be noted that

considerable effort was put into adjusting parametersthat determine cloud properties in the standard modelso as to achieve reasonably good agreement, in a zonalmean sense, with observed radiative forcing, particu-larly in the Tropics. The response to implementation ofthe new parameterizations must be viewed in this con-text. An operational implementation of one of the newparameterizations would in general require a reviewand retuning of other parameterizations to achieve asimilarly acceptable agreement with observations.However, there is no evidence to suggest that the simu-lations based on the mean effective size of ice particles,which was parameterized as a function of both tem-perature and IWC, agree better with observations ascompared to the Dge parameterized as a function oftemperature alone. It is also noteworthy that in theTropics the IR forcing for the CCCma standard simu-lation is closer to that for the simulation using the newparameterization without including small ice crystals.This is consistent with the curves in Fig. 6, which showsthe mean effective ice crystal size parameterized as afunction of IWC and temperature in this work and byMcFarquhar (2001) based on measurements in tropicalcirrus clouds formed in a region of convective outflowgiven as

Dge�IWC, T� � 10�a�T��b�T���c�T��2�d�T��3 , �4�

where � � IWC/IWC0, and the coefficients a, b, c, andd are dependent on temperature (see McFarquhar 2001for more details), and IWC0 � 1. The CCCma GCM3

FIG. 4. The global distribution of the anomaly in the planetary albedo for DJF.

FIG. 3. The percent change in the effective ice crystals size dueto adding small ice crystals (R), and the ice crystal size with (with-out) small ice particles Dge�s(Dge) plotted against temperature.The tropical parameterization given in Garrett et al. (2003)(G2003) is also given.

3534 J O U R N A L O F C L I M A T E VOLUME 20

Fig 4 live 4/C

uses the effective size parameterization with IWC aloneby Lohmann and Roeckner (1996), which is given asDge � 129.06 IWC0.216 and later adapted with sometuning in a form

Dge � max�min�129.06 IWC0.216, 77�, 31 . �5�

The Lohmann and Roeckner (1996) parameterization,with limitations as noted above, is also shown in Fig. 6.If the tropical Dge is mainly determined by IWC, forhigh IWCs, which would be expected in a tropical cirruscloud formed in a convective outflow region, the newparameterization with small ice crystals would under-estimate the effective size and overestimate the opticaldepth. This would partly explain the more pronounced

IR cloud forcing in the Tropics. Observations in mid- tohigh-latitude regions indicate that Dge has a weak IWCdependence, but the Dge in tropical clouds as reportedby McFarquhar (2001) shows very strong IWC depen-dence. In contrast the observations reported by Garrettet al. (2003), also in tropical clouds, suggest that the Dge

mainly depends on temperature in basic agreementwith Boudala et al. (2002; Fig. 3). It is difficult to com-pare Dge (IWC) directly with the parameterizationgiven in Fig. 3, which depends only on temperature.However, in ice clouds, IWC generally increases withincreasing temperature (Boudala et al. 2002; Field et al.2004; Stephens et al. 1990; McFarquhar and Heymsfield1997). Thus, one can expect larger Dge with increasing

FIG. 5. Seasonally and zonally averaged IR cloud forcing (W m�2) in DJF. (top) Based on a 5-yrsimulation without small crystals and with small ice crystals as indicated by symbols (left) Dge(T ) and(right) Dge�s(T ), respectively. (bottom) (left) The standard CCCma GCM3 simulations for the sameseason and (right) the simulations based on the mean effective size parameterized as a function oftemperature and ice water content, Dge�s(T, IWC). The satellite observation is marked by a dashed lineand the model result is marked by a solid line.

15 JULY 2007 B O U D A L A E T A L . 3535

IWC or increasing temperature. The possible ranges ofthe Dge (30–77 �m) in simulations using the operationalversion of AGCM3 are similar to Dge(T) derived with-out small ice particles, as can be seen in Fig. 6. Whensmall particles are included, however, for a given cloudwith predicted IWCs (IWC � 0.002 g m�3 or IWC 0.1g m�3), Eq. (5) may predict Dge of 31 or 77 �m, respec-tively, and these may not be compatible with Dge pre-dicted by Dge�s(T), which never exceeds 46 �m in sub-freezing temperatures. Tropical ice clouds containIWCs much higher than 0.1 g m�3, and thus it is notsurprising to see the significant differences betweenthe two simulations in the Tropics that are depicted inFig. 5.

b. Sensitivity in solar radiation

Figure 7 shows the mean DJF shortwave cloud forc-ing for the five simulated years as mentioned in theprevious section. As in the case of the IR cloud forcing,the effect of small ice crystals in shortwave cloud forc-ing is larger in the Southern Hemisphere Tropics byabout 10 W m�2. This is consistent with changes in theplanetary albedo noted in the preceding section andexpected as a consequence of including small ice crys-tals, which on average reduces the mean effective sizesof ice crystals. Since optical depth increases with de-creasing Dge for a given IWC, this causes more solarradiation to be reflected back to space.

Generally, the operational version of AGCM3 pre-dicts less shortwave cloud forcing than observed in theextra Tropics of the summer hemisphere. The new pa-rameterizations that include small ice particles seem toalleviate this deficiency slightly. It should be noted thatzonal averaging eliminates the substantial spatial vari-ability of cloud forcing associated with the differentparameterization of Dge. As discussed in the previoussections, localized effects of small particles on the ra-diation field are much larger than is evident in the zon-ally averaged fields.

The potential importance of accounting for smallparticles in parameterization of ice crystal effectivesizes, particularly in the Tropics, has been demon-strated by these results. Results of the simulations forother seasons show very similar behavior although thestrength of the forcing changes can differ.

c. Sensitivity in net radiative forcing

Adding small ice crystals in the radiation parameter-ization has two potential effects in the atmospheric ra-diation budget. It increases the IR absorption, whichtends to warm the atmosphere, and it enhances thescattering of solar radiation, which tends to cool theatmosphere. It is the net energy balance (�E) at the topof the atmosphere that determines whether the atmo-sphere is on average warming or cooling. This net en-ergy balance at the TOA is defined as the differencebetween the energy (mainly solar) that is entering theatmosphere and the thermal (IR) energy that is leavingthe atmosphere. Figure 8 shows a model-simulated glo-bal distribution of the difference in net energy balance{�E[Dge(T)] � �E[Dge�s(T)]} at the TOA between thesimulation without small ice particles [�E[Dge(T)]] andwith small ice particles [�E[Dge�s(T)]] for an averageof five simulated years. Comparison of JJA with DJFshows that the anomaly is relatively larger in the Trop-ics, and in a winter season in both hemispheres, par-ticularly in the Northern Hemisphere winter (DJF),shows mostly negative trends reaching up to �10 Wm�2 in some localized regions over the North Atlanticand Indian Oceans. The simulated and observed netenergy balance at the TOA is negative in the winterhemisphere (net energy loss) and positive in the sum-mer hemisphere (net energy gain). Therefore, the nega-tive trend in the figure implies that �E[Dge(T)] is morenegative than �E[Dge�s(T)] in the winter hemisphereand more energy is lost to space in the absenceof small ice crystals. However, during the summer hemi-sphere the negative trend implies that �E[Dge�s(T)] ismore positive than �E[Dge(T)], which also implies thatthe atmosphere gains more energy in the presence ofsmall ice crystals. In winter, the incoming solar ra-

FIG. 6. Comparisons of mean effective ice crystal size param-eterized as function IWC and temperature in this work and byMcFarquhar (2001) for tropical cirrus. The effective size param-eterization with IWC alone used by Lohmann and Roeckner(1996) and later adapted in CCCma GCM3 with some tuning isalso shown.

3536 J O U R N A L O F C L I M A T E VOLUME 20

diation is reduced in both hemispheres, but the IR fluxis relatively unchanged. This may be one part of thereason why the effect is much stronger in the winterseason as compared to the summer season. It shouldalso be noted, however, that the strongest effects arevery much localized, and it is perhaps noteworthy thatthe spatial patterns of energy balance anomalies in Fig.8 have some similarities to those of OLR. In DJF, overthe North Atlantic, Indian Oceans, and southern Af-rica, the strong reductions in outgoing IR fluxes arecorrelated to the minimum in energy loss shown in Fig.8. In JJA (see Figs. 1 and 8), for example, over north-western Africa, the eastern and western coasts of theSouth American continent, and some parts of the In-dian Ocean a similar behavior is shown suggesting thatthe reduction in IR flux due to adding small particlesplays a significant role in the seasonal radiative energybalance of the globe.

In DJF, the global mean energy balance at the TOAwas calculated to be 10.6 W m�2 with small ice crystals,but without small ice crystals it was 9.5 W m�2. Thismeans that on average the atmosphere gains a net en-

ergy of 1 W m�2 in that period due to adding small icecrystals. The calculated energy balance difference atthe ground was almost twice as large, implying a cor-responding reduction in net energy lost to the groundby the atmosphere. In JJA, the net change in energybalance at the top of the atmosphere was about �1 Wm�2, similar in magnitude to that in DJF but with anopposite sign, but at the ground the net change is re-duced to 1.3 W m�2. However, the 5-yr globally aver-aged energy balance (for all seasons combined) at theTOA was �0.3 W m�2 for the model simulations with-out small particles, which is similar to the CCCma stan-dard control simulation (see section 3a), and 0.8 W m�2

when the small particles are included. Both of thesevalues are relatively small and well within the uncer-tainty of satellite measurements of the TOA radiationbalance.

The net global mean cloud forcing at the TOA in JJAwas �21.4 W m�2 for the simulation without small icecrystals as compared to �19 W m�2 when the smallparticles are added. The difference of about 2.4 W m�2

is substantial relative to the simulated forcing. For DJF

FIG. 7. Seasonal and zonally averaged shortwave cloud forcing (W m�2) in DJF. Symbols are asin Fig. 5.

15 JULY 2007 B O U D A L A E T A L . 3537

the net cloud forcing is �20.5 and �22.2 W m�2 withand without small ice crystals, respectively, with aslightly lower difference of 1.7 W m�2. The globallyaveraged 5-yr mean values of cloud radiative forcing,cloudiness, precipitation, and temperature are given inTable 1. The change in globally averaged 5-yr meancloud forcing due to adding small ice crystals is close to1.9 W m�2. The globally averaged precipitation de-creased by about 8% when small ice crystals wereadded, resulting in slightly better agreement with ob-servations. In contrast to precipitation, cloudiness in-creased slightly by about 2% when small particles were

included. The global mean surface (screen) tempera-ture also increased slightly (by about 0.2°C) when smallice particles were included.

4. Summary and conclusions

Parameterizations of effective sizes of ice crystals asa function of temperature, IWC, and temperature withand without small ice crystals (D � 100 �m) have beentested using the Canadian Climate Centre for ClimateModelling and Analysis (CCCma) third-generationgeneral circulation model (GCM3). In this study, a 5-yr

FIG. 8. Seasonally averaged global distribution of anomaly in energy balance �E[Dge(T )] ��E[Dge�s(T )] at the top of the atmosphere based on a 5-yr simulation (top) for DJF and (bottom) forJJA.

3538 J O U R N A L O F C L I M A T E VOLUME 20

Fig 8 live 4/C

mean seasonally averaged dataset has been used to de-pict the effects of implementing these parameteriza-tions.

The simulation results indicate that the addition ofsmall ice particles in parameterizations of effective sizegives rise to two notable effects in climate simulations.First they inhibit the loss of IR radiation to space and,second, they enhance the scattering of solar radiation.On average, these two effects counteract each other,but seasonal averaged global distribution of energy bal-ance data shows that the small ice crystals make cloudsmore opaque to IR radiation. This effect is stronger inthe winter hemisphere. The simulation with Dge thatcontained small ice crystals gave higher cloud forcing(IR and solar) in the tropical cloudy regions as com-pared to both the operational simulation and the satel-lite observations. As noted in the foregoing discussion,this enhanced departure from observations is not unex-pected because the operational parameterizations havebeen tuned to achieve reasonably good (zonal mean)agreement with the observed forcing in the Tropics.However the sensitivity of the simulated cloud radiativeforcing to inclusion of small ice particles is demon-strated to be substantial. Although there have beensome changes in cloudiness, precipitation, and tempera-ture, these differences are relatively small. Thus muchof the more pronounced differences in forcing in theTropics are associated with the fact that the simulatedice clouds in the tropical upper atmosphere are found athigher levels and are colder than the clouds found athigh latitudes. Therefore, since the contribution ofsmall ice particles to the effective size of ice crystalsincreases with decreasing temperature, the parameter-ization that includes small particles predicts smaller ef-fective sizes of ice crystals and thus higher cloud forcingin tropical cirrus as compared to midlatitude cirrus.

Model simulations based on the new parameteriza-tions, which include small ice particles, overestimatedthe effects of both longwave and shortwave forcing atthe top of the atmosphere in the Tropics where thesignificant high clouds are formed, as compared to ob-servations. As noted above, this locally larger departurefrom observations is not unexpected in simulations

where a particular parameterization is replaced withoutany corresponding changes in linked parameterizations.However, it is also possible that the effective sizes of icecrystals (Dge) in some tropical cloud regimes are inher-ently larger, as has been demonstrated by McFarquhar(2001), and thus underestimated by parameterizationsused in this work. This may be so notwithstanding thatthe tropical Dge values reported by Garrett et al. (2003)are in relatively good agreement with the proposed pa-rameterization, which includes the effects of small par-ticles.

The results indicating that simulated cloud radiativeforcing is substantially affected by including the effectsof small particles underline the importance of takingthese effects into account in future model development.The possibility of applying the proposed single Dge pa-rameterization for the entire globe, while appealing be-cause of its simplicity and ease of implementation, re-quires further study to determine its range of applica-bility and reliability. However, introduction of a morecomplicated parameterization that attempts to accountfor different cloud regimes in a physically meaningfulway requires a corresponding enhancement in the treat-ment of clouds in general and microphysical processesin particular. Such developmental activities are cur-rently under way within CCCma in regard to construc-tion of a newer version of the AGCM, which, amongother things, employs a prognostic cloud scheme that isquite different in its formulation and implementationfrom that used in AGCM3 and explicitly predicts liquidand ice water contents. Preliminary tests using the pro-posed new parameterization for effective size with thecurrent experimental version of this new model havequalitatively corroborated the AGCM3 simulations dis-cussed in this paper.

Acknowledgments. This work was funded by the Ca-nadian Foundation for Climate and Atmospheric Sci-ences (CFCAS), the National Science and EngineeringResearch Council (NSERC), the National Search andRescue Secretariat (NSRS), Transport Canada, thePanel on Energy Research and Development (PERD),and the Canadian Climate Action Fund (CCAF), as

TABLE 1. Five-year mean globally averaged temperature, precipitation, cloudiness, and net radiative forcing based on simulationswithout small particle (Dge) and with small ice particles (Dge�s). The observed (obs) values of cloudiness based on the ISCCP andprecipitation based on the Global Precipitation Climatology Project (GPCP) are also given.

Dge Dge�s. Dge�s � Dge Obs Dge�s � obs

Precipitation (mm day�1) 2.84 2.76 �0.08 2.71 GPCP 0.05Cloudiness 0.61 0.63 0.02 0.62 ISCCP 0.01Temperature (°C) 14.2 14.4 0.2Cloud forcing (W m�2) �20.6 �18.7 1.9

15 JULY 2007 B O U D A L A E T A L . 3539

well as from U.S. sources including the Boeing Com-mercial Airplane Group, the National Aeronautics andSpace Administration (NASA), and the Federal Avia-tion Administration (FAA). The data were collectedusing the Canadian National Research Council (NRC)Convair-580, and the authors are grateful to their NRCcolleagues for their assistance. The authors also wouldlike to thank Dr. John Scinocca and Fouad Majaess fortheir technical support during this work at the Cana-dian Centre for Climate Modelling and Analysis(CCCma) in Victoria, Canada.

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